The Lifting Wavelet Transform for Periodogram Smoothing
M. Venakatanarayana, T. Jayachandra Prasad · 2012
The wavelet thresholding technique is an effective way of obtaining a smoothed non parametric spectrum estimate of a stationary signal. This approach has ability to capture statistically significant components of In ) ( ln f S at different resolution levels and guarantees non negativity of the spectrum estimator. This technique solves the problem of specified noise/resolution tradeoffs by treating the wavelet coefficients of the additive noise as independent random variables. In this paper an attempt has been made to propose a new technique to estimate the smooth spectra based on Lifting wavelet transform via thresholding.The selection of thresholds are based on 1) Gaussian approximation 2) Stain’s Unbiased Risk Estimator (SURE). The variance in the estimation of smooth spectra based on proposed methods is in agreement with those obtained by normal wavelet transform at the benefit of computational time.